PrintLevel 0: no output
PrintLevel 1+: some basic information each loop (no polynomials): computation degree, number of S-pairs, number of new generators, termination conditions.
PrintLevel 2+: basic polynomials: S-pairs and new sagbi generators
PrintLevel 3+: extra polynomials: reduction ideal generators, zeroGens, current sagbi generators
PrintLevel 4+: show the input and output of each subduction
Higher levels exist but may be overly verbose. PrintLevel 5 shows the processPending data and PrintLevel 6 shows the intermediate steps for top-level subduction.
The object PrintLevel is a symbol.